Advertisements
Advertisements
प्रश्न
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right)\] , then \[f\left( \frac{2x}{1 + x^2} \right)\] is equal to
पर्याय
(a) {f(x)}2
(b) {f(x)}3
(c) 2f(x)
(d) 3f(x)
उत्तर
(c) 2f(x)
\[ = \log \left( \frac{\frac{1 + x^2 + 2x}{1 + x^2}}{\frac{1 + x^2 - 2x}{1 + x^2}} \right)\]
\[ = \log \left( \frac{(1 + x )^2}{(1 - x )^2} \right)\]
\[ = 2 \log \left( \frac{1 + x}{1 - x} \right)\]
\[ = 2 (f(x))\]
APPEARS IN
संबंधित प्रश्न
Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
Find the range of function.
Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + g, f − g, fg and \[\frac{f}{g}\] .
Let f(x) = x2 and g(x) = 2x+ 1 be two real functions. Find (f + g) (x), (f − g) (x), (fg) (x) and \[\left( \frac{f}{g} \right) \left( x \right)\] .
Write the domain and range of function f(x) given by
Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =
The domain of definition of \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is
The domain of definition of the function f(x) = log |x| is
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
Check if the following relation is function:
If f(m) = m2 − 3m + 1, find f(− x)
A function f is defined as follows: f(x) = 4x + 5, for −4 ≤ x < 0. Find the values of f(−1), f(−2), f(0), if they exist.
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 1), (2, 1), (3, 1), (4, 1)}
Check if the relation given by the equation represents y as function of x:
2x + 3y = 12
If f(m) = m2 − 3m + 1, find f(−3)
If f(m) = m2 − 3m + 1, find f(− x)
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x3
Show that if f : A → B and g : B → C are onto, then g ° f is also onto
Write the following expression as a single logarithm.
ln (x + 2) + ln (x − 2) − 3 ln (x + 5)
Prove that logbm a = `1/"m" log_"b""a"`
Solve for x.
log2 x + log4 x + log16 x = `21/4`
Select the correct answer from given alternatives.
If f(x) =`1/(1 - x)`, then f{f[f(x)]} is
Answer the following:
Find whether the following function is one-one
f : R → R defined by f(x) = x2 + 5
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3
Answer the following:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Answer the following:
If b2 = ac. prove that, log a + log c = 2 log b
Answer the following:
Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2
Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on N. Find the domain, co-domain and range. Is this relation a function?
Given the function f: x → x2 – 5x + 6, evaluate f(2)
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
| Length ‘x’ of forehand (in cm) |
Height 'y' (in inches) |
| 35 | 56 |
| 45 | 65 |
| 50 | 69.5 |
| 55 | 74 |
Find a and b
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
Let f and g be two functions given by f = {(2, 4), (5, 6), (8, – 1), (10, – 3)} g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)} then. Domain of f + g is ______.
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f + g)(x)
Domain of `sqrt(a^2 - x^2) (a > 0)` is ______.
The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.
Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x2 – 2x, and g(f(x)) = 4x2 + 6x + 1, then the value of f(2) + g(2) is ______.
If f : R – {2} `rightarrow` R i s a function defined by f(x) = `(x^2 - 4)/(x - 2)`, then its range is ______.
The period of the function
f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` is ______.
The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.
